Two Port Networks
By
Mr. Aniket Kumar
Assistant Professor, Department of Electronics & Communication Engineering
Shobhit Institute of Engineering & Technology (Deemed to-be University)
NH-58, Modipuram, Meerut – 250 110, India
Chapter-5
Two port networks
A two-port network is a four- terminal circuit in which the terminals are paired to form an input port and
an output port. Different models for two port networks are
Model Name
Express
In terms of
Defining equations
Impedance
V1, V2
I1, I2
V1= z11I1 + z12I2 and V2= z21I1 + z22I2
Admittance
I1, V2
V1, V2
I1= y11V1 + y12V2 and I2= y21V1 + y22V2
Hybrid
V 1, I 2
I1, V2
V1= h11I1 + h12V2 and I2= h21I1 + h22V2
Transmission
V 1, I 1
V2, -I2
V1= AV2 – BI2 and I1= CV2 – DI2
Hybrid Parameters
Every linear circuit having input and output terminals can be analyzed by four parameters (one measured
in ohm, one in mho and two dimensionless) called hybrid or h Parameters. Hybrid means “mixed”. Since
these
parameters
have
mixed
dimensions,
they
are
called
hybrid
parameters.
Transistor is a three terminal device but for practical purpose it need four terminals two used for input &
two for output.
Nomenclature for Transistor h Parameters
S. No.
h parameter
Notation in CB
Notation in CE
Notation in CC
h11
hib
hie
hic
1.
h12
hrb
hre
hrc
2.
h13
hfb
hfe
hfc
3.
h14
hob
hoe
hoc
4.
Q.1.
Long & Short Questions
Explain the meaning of h-parameter of a transistor . Write down all h- parameters in
different configurations. How will you obtain h- parameter of a transistor in CE
configuration with the help of the characteristic curves ?
Or
What do you understand by hybrid parameters of a transistor ? [Important]
Or
What is the significance of hybrid parameters ? Define them. How they are determined ?
Every linear circuit having input and output terminals can be analyzed by four parameters (one
measured in ohm, one in mho and two dimensionless) called hybrid or h Parameters. Hybrid
means “mixed”. Since these parameters have mixed dimensions, they are called hybrid
parameters.
Consider a linear circuit shown in figure. This
circuit has input voltage & current labeled v1 & i1
and output voltage & current as v2 & i2 .
Hear both the inputs are assumed to flow into the
box.
Determination of h- parameters
From the advance circuit theory voltages and currents in figure can be related by the following
set of equations :

v1 = h11 i1 + h12 v2
………. (i)
i2 = h21 i1 + h22 v2
………. (ii)
If we short- circuit the output terminals, we have v2= 0
Applying these changes in above equations we have
v1 = h11 i1 + h12 x 0
i2 = h21 i1 + h22 x 0
∴
h11 = v1/ i1 for v2=0
h21 = i2/ i1 for v2=0

If we open the input terminals, we have i1= 0
Applying these changes in above equation (i) & (ii) we have
v1 = h11 x 0 + h12v2
i2 = h21 x 0 + h22 x v2
∴
h12 = v1/ v2 for i1=0
h21 = i2/ v2 for i1=0
Q.2.
Define h- parameter for different configuration of a transistor . How are these determined
experimentally ? Draw the hybrid equivalent circuit for any one configuration .
For definition refer to Q.1.
Hybrid equivalent circuit of a transistor
For small a.c. sigals, the transistor behaves as a linear device because the output a.c. signal is
directly proportional to the input a.c. signal. Under such circumstances, the a.c. operation of the
transistor
can be
described
in terms
of
h
parameters.




To describe the external behavior of transistor amplifier four quantities are required ,
these are v1, i1, v2 and i2 .These voltage & current are related as the following equations :
v1 = h11 i1 + h12 v2
………. (i)
i2 = h21 i1 + h22 v2
………. (ii)
The values of h parameters of a transistors will depend upon the transistor connection
(i.e. CB , CE or CC) used.
The values of h- parameters depend upon the operating point. If the operating point is
changed , parameter values also changes.
The notation v1 ,i1, v2 and i2 are used for general circuit analysis. In a transistor amplifier,
we use the notation depending upon the configuration in which transistor is used. Thus
for CE arrangement.
v1 = Vbe ; i1 = Ib ; v2=Vce ; i2=Ic .
Here Vbe, Ib , Vce & Ic . are the rms values .
Nomenclature for Transistor h Parameters
S. No. h parameter
Notation in CB
1.
h11
hib
2.
h12
hrb
3.
h13
hfb
4.
h14
hob
Transistor Circuit Performance in hParameters
(i)
Notation in CE
hie
hre
hfe
hoe
Notation in CC
hic
hrc
hfc
hoc
Input impedance : The general expression for input impedance is
Zin= h11- (h12h21)/ (h22+ 1/ rL)
For CE Configuration
Zin= hie- (hrehfe)/ (hoe+ 1/ rL)
Similarly , expressions for input impedence in CB & CC arrangements can be written.
(ii)
Current gain : The general expression for current gain is
Ai = h21/(1+h22rL)
For CE Configuration
Ai = hfe/(1+hoerL)
(iii)
Voltage gain : The general expression for voltage gain is
AV= -h21/ [Zin(h22 + 1/ rL)]
For CE Configuration
AV= -hfe/ [Zin(hoe + 1/ rL)]
(iii)
Output impedance : The general expression for output impedance is
Zout= [h22- h21.h12/ h11]-1
For CE Configuration
Zout= [hoe- hfe.hre/ hie]-1
Q.3.
Explain two Port network & Y-parameters of a transistor.
Related Short Answer Questions
(i)
Explain Y-parameter of a transistor .
Two port network explained in Q- 1 & Q-2
Admittance parameters or Y-parameters are the properties used in many areas of electrical
engineering, such as power, electronics, and telecommunications. These parameters are used to
describe the electrical behavior of linear electrical networks. They are also used to describe
the small-signal (liberalized) response of non-linear networks.
The equations describing admittance parameters are
I1= y11V1 + y12V2
I2= y21V1 + y22V2

If we short- circuit the output terminals, we have v2= 0
Applying these changes in above equations we have
I1= y11V1 + y12 x 0
I2= y21V1 + y22 x 0
∴
y11 = v1/ i1 for v2=0
y21 = i2/ v1 for v2=0

If we short the input terminals, we have v1= 0
Applying these changes in above equation (i) & (ii) we have
I1= y11 x 0 + y12V2
I2= y21 x0 + y22V2
∴
y12 = I1/ v2 for i1=0
y22 = i2/ v2 for i1=0
Numerical
Q.1.
Find the h- parameters of the circuit shown
Exp: Considering all the output terminals to be shorted , the input impedance under this condition
is the parameter h11
∴ h11= 4 + 4 ⃓⃓ 4 = 4 + 4.4/(4+4)= 6Ω
∵ Input current i1 will be divided equally between ll connected resitances
∴ i2= - i1/2= -0.5i1
∵ h21 = i2/ i1
∴ h21 = i2/ i1 = -0.5 i1/ i1 = -0.5
In order to find h12 & h22 , with input open circuited we have
Under this condition , we have v1 = 4 Ω . V2 / (4 Ω+ 4 Ω) = 0.5 x V2
∵ h12 = v1 /v2= 0.5 i1/ i1 = 0.5
Looking into the output terminals with input terminals open, the output impedance is 8 Ω
∴ h22 = 1/8 = 0.125 mho
Q.2.
Figure shows the transistor amplifier in CE arrangement. The h parameters of transistor
are as under :
hie= 1500 Ω; hfe= 50; hre = 4 ×10−4 ; hoe = 5 ×10−5 mho
Find (i) a.c. input impedance of the amplifier
(ii) voltage gain
(iii) output impedance.
Exp: The a.c. load rL seen by the transistor is equivalent of
the parallel combination of RC(= 10 kΩ & RL= 30 kΩ
i.e. rL=10 x 30/ (10+ 30) =7.5 k Ω
(i)
(ii)
(iii)
The input impedance looking into the base of transistor is given by :
Zin= hie- (hrehfe)/ (hoe+ 1/ rL)
Putting the respective values
Zin= 1390 Ω
Voltage gain i.e. AV= -h21/ [Zin(h22 + 1/ rL)]
Putting the respective values
AV= -196
Output impedance i.e. Zout= [hoe- hfe.hre/ hie]-1
Putting the respective values
Zout= 5.88 K Ω
Q.3.
A silicon transistor with VBE(sat)= 0.8 V , β= hFE= 100, VCE(sat)= 0.2 V is used in the circuit shown.
Find the minimum value of RC for which the transistor remains in saturation.
Exp: Given VBE(sat)= 0.8 V , β= hFE= 100 & VCE(sat)= 0.2 V
Applying KVL at the input terminal , we have
-5V + 200k. IB + 0.8V =0
∴ IB = 4.2/ (200 x 103) = 21μA
∵ IC =β IB= 100 x 21μA = 2.1mA
Applying KVL at the output terminal , we have
-10 + RC IC + VCE(sat)= 0
∴ RC = (10- 0.2) / 2.1mA = 4.667kΩ Ans